Prior to the initial experimentation with double-finned surfboards in the early 1970's, a single center fin, located at the very tail of the board, provided the directional stability essential to the basic performance of the board. Since the advent of tri-fin or “thruster” type surfboards in the early 1980's, high-performance surfboards have also incorporated two side-fins to dramatically increase the board's speed and maneuverability. The side-fins are located on opposite sides of the board near the perimeter edge or “rail,” and well forward of the single, central trailing fin at the tail.
In the tri-fin configuration, it is well established that the center fin is primarily a stabilizing fin and functions in a manner very similar to the fixed keel on a sailboat or the vertical stabilizer on an aircraft—i.e. if the board yaws or departs from its original heading, the rotation of the board causes the water-flow to strike the fin at an angle; this creates a low-pressure area on the opposite or lee side of the fin that resists the yaw, and allows directional stability to be maintained.
Knowledge is still very limited, however, as to how the side-fins enhance the speed and maneuverability of modern multi-finned type boards. This has long been a major problem in surfboard design. As a result, the first, largely experimental “twin-fin” and “fish” style surfboards, the double-finned predecessors of the modern tri-fin, suffered for many years from a variety of poorly understood control problems. The early control problems—which were collectively referred to as “tracking”—were found to be greatly reduced by using a negatively angled side-fin setting. Although this eliminated the original tracking problem, it also caused an overly loose, drifting type of turn that many riders, even at the expert level, found very difficult to control. Eventually, the problem was remedied by adding a third stabilizing fin at the very tail of the board, the configuration in current use today. Though much faster and more maneuverable than the single-finned board types that preceded it, the current tri-fin setting was arrived at almost entirely through trial and error; as a consequence, it retains features that actually contribute to a marked increase in drag. The main drawbacks of prior art tri-fins may be summarized briefly as follows:
Each side-fin is set at a negative angle of attack or “toe-in” angle of between three and five degrees, so that the leading edge points in the approximate direction of the longitudinal centerline at the nose. The angle is measured using the chord line (a straight line drawn through the leading and trailing edges of the fin at the fin base), which is referenced to the longitudinal centerline provided by the wooden center spar or “stringer” that runs the length of the board. The negative angle of attack or toe-in causes the water-flow to strike the side-fins at an angle, and creates high drag from the “snowplow” effect when the rider's weight is neutrally centered on the board.
The cambered foil of the side-fin adds to this drag: in the longitudinal cross-section view commonly used to depict the airfoil section of a wing, the foil of the side-fin is asymmetrical, and has an average curvature greater on one side than the other. The foil of the conventional prior art side-fin is flat to slightly concave on the inside surface (the side facing the longitudinal centerline or stringer), and curved on the outside (the side facing the perimeter edge or “rail”). Although the cambered side-fin foil appears to give better performance and greater average speed, knowledge is currently very limited as to the reasons why, since both the flat-sided, and particularly the slightly concave side-fin foil, would appear to greatly increase the drag from the negative toe-in angle. It is well known that separation of the boundary layer and turbulence occurs more readily when a flat or concave surface is set at an angle to a fluid flow, versus a symmetrical foil, for example, where both sides are convex and curve equally in opposite directions in a low-drag, streamlined shape.
Currently, the rider can overcome the high drag of the side-fin setting by constantly turning the board. As noted above, the high drag condition occurs primarily when the rider's weight is neutrally centered on the board—the drag is reduced, however, when the rider leans to initiate a turn and lifts the opposing side-fin free; the angle of the side-fin remaining in the water then acts like a deflected rudder and aids the board's rotation in the turn; on a tri-fin board, the rider's normal weight shift further in the turn will then set the center stabilizing fin, and prevent the overly loose, difficult to control, drifting type of turn that, subsequent to the “tracking” problem, was the major drawback that greatly limited the acceptance of the early double-finned style boards. Surfboard designers have long noted that adding a third stabilizing fin does little to diminish the maneuverability of the board—it instead produces such a noticeable burst of speed and acceleration in a turn that, in the early development of the tri-fin, the center stabilizing fin almost immediately came to be referred to as “thruster” fin, and the tri-fin set-up as a “thruster” type board. In the tri-fin or thruster configuration, however, the addition of the center stabilizing fin causes a third and final drawback:
The location of the center stabilizing fin is precisely the opposite of the optimum theoretical configuration: i.e., if the negatively angled side-fin functions as a deflected rudder, it should be placed as far behind the board's axis of rotation as possible so as to increase its moment arm; the added leverage would lessen the surface area of the side-fin and the amount of negative toe-in angle required for a given turning moment, and thereby reduce drag. Locating the fin or fins required for directional stability forward of a negatively angled trailing fin, closer to the axis of rotation, would increase the directional instability of the fin-setting by allowing the negatively angled rearward fin to truly function as a permanently deflected rudder. Failure to correct the drawbacks outlined above, and the absence of innovation regarding fin placement on multi-fin type boards (the group includes other multi-finned variants, e.g., “twinzers,” “quads,” “fishes,” etc. all of which use the negatively angled side-fin setting), is largely due to the poor understanding of the role the fins play in enhancing the performance of the board. Despite the high speed and exceptional maneuverability of modern multi-finned boards vs. the early single-finned board types, at present, their higher performance actually comes at a cost of considerable drag. From a hydrodynamic standpoint, it can be seen that the board-making arts currently have need of a cambered side-fin foil that exhibits reduced drag at the conventional negatively angled side-fin setting, as well as multi-fin arrangements that will introduce directional instability, but at a reduction in drag over the multi-fin configurations of the prior art.
The following description is intended to impart an understanding of the present invention to a person skilled in the art of surfboard design. Those skilled in the art, however, will be aware of the current lack of tank-testing facilities, and the absence of any method that can accurately duplicate a breaking wave, the movement of the board on a wave, or the effects of the rider maneuvering the board in a controlled setting. Therefore, at least some of the material disclosed herein is a subjective interpretation of observed phenomena, and the descriptions provided below should not be interpreted in a way that will limit the invention, which is defined more fully and accurately in the appended claims.
At the time the present invention was made, the board-making arts lacked an explanation for the clearly superior performance of multi-finned type boards. As will be appreciated by those skilled in the art upon reviewing the disclosure below, the much higher speed of currently available multi-finned boards can be largely attributed to the higher lift coefficient of the cambered side-fin foil. The following detailed description of the invention therefore begins with a discussion of the relationship between the (hydro-) foil of the fin, and the airfoils of a wing and a sail, which respond in similar ways to a fluid flow despite the differing densities between air and water.
Sailboats and aircraft are able to maneuver because of the differential “lift” of a plurality of separate air- and hydrofoils at differing angles of attack: on a sailboat, for example, the “lift” of the deflected rudder creates a yawing moment behind the fixed keel that causes the sailboat to rotate in a turn; on an airplane, the differential lift between the wing and the horizontal tail (as altered by deflected control surfaces such as ailerons, elevons, the elevator, etc.) makes it possible for the aircraft to execute banked turns and fly in a loop. The board-designer, therefore, may use the same principles and analyze the angle of attack of the fin(s) relative to the direction of the water-flow through a turn, and arrange the fins, and the foil of the fins, to optimize the speed and performance of the multi-finned board as it is maneuvered on a wave.
Board designers may therefore benefit from a fuller knowledge of the similarities between the hydrofoil of the fin and the airfoil of the wing and sail, and make use of the extensive aeronautical research that has been compiled comparing the performance of various airfoil sections at different wind speeds and angles of attack. As shown in greater detail below, aeronautical engineers have developed sophisticated means of accurately measuring the performance of a wing; typically, the relevant wind tunnel data are plotted in graph form or, as shown in FIG. 1A and FIG. 1B, by using vectors, in which the length and direction of an arrow indicates the magnitude and direction of the force of the air pressure, or pressure field, that develops around the airfoil of a wing in response to its incidence, or angle of attack, relative to the airstream. For illustration purposes, the vectors shown in FIG. 1A and FIG. 1B, which actually represent the pressure differential around the airfoil of a wing, will be assumed to be completely interchangeable with the flat-sided cambered side-fin foil of the prior art. In addition, although the foils in FIG. 1A and FIG. 1B are depicted in a vertical orientation, in the following discussion they will be referred to as being in a horizontal position when the description is of an airfoil in flight, while the fluid flow F will be understood to represent both air- and water-flow.
In FIG. 1A, the vectors shown represent the pressure differential typically seen around the airfoil of a wing at cruise, when the airstream or airflow F is almost parallel to the airfoil of the wing. Ordinarily, the aircraft is designed so that the airplane's fuselage is completely level under normal flight conditions for minimum drag, while the wing is positioned at a very low but slightly positive angle of attack (e.g., typically about two degrees), so that the highest pressure will be at the leading edge of the wing, as shown, while the much lower pressure on the upper surface of the airfoil holds the aircraft aloft.
In aircraft design, a basic problem is that the pressure field depicted in FIG. 1A is unequal; as a result, the wing has a “pitching moment” and the aircraft tends to nose downward until the pressure around the wing is equalized. To prevent this, a horizontal stabilizer is provided at the tail, the airfoil of which is set at a slightly negative incidence or angle of attack so as to provide steady downward pressure, which counters the pitching moment of the wing and allows the aircraft to remain in steady, level flight.
Comparing the foil of a board fin to the airfoil of the wing, it can be assumed that a parallel side-fin setting will create a “yawing moment” similar to the pitching moment of the wing, and create control problems that would require a negatively angled trailing fin to counter, assuming the example set in aircraft design is followed. In surfboard design, however, the “tracking” problems exhibited by the very early fish style boards, which originally used a parallel side-fin setting, were eliminated by changing the fin position so the side-fin was fixed at a negative angle of attack. Despite the high drag and snowplow effect of the now standard, negatively angled side-fin setting, the modern multi-finned board type is much faster than the single-finned board types that preceded it. As will be appreciated by those of skill in the art after reading the disclosure below, this is because the rotation of the board in a turn places the side-fin foil at a high angle of attack, and a pressure differential forms around the fin that is much like the airfoil of a wing or sail at a similar angle of attack, as described in greater detail below.
In FIG. 1B, the pressure differential shown is typical of an airfoil at a very high angle of attack, when the airflow F is striking the underside of the wing, as is the case when the aircraft is flying in a loop or pulling out of a dive. Note that in either case the motion of the aircraft describes an arc, and that the direction of the airflow F is almost entirely due to the motion of the aircraft itself (assuming a still day with little breeze). When the airfoil is at a high angle of attack as shown, a very large area of negative pressure develops around the leading edge of the airfoil and pulls the wing forward. It is known that a similar area of low-pressure around the forward portion of a sail drives a sailboat forward and enables it to sail into the wind. From FIG. 1B, it can be assumed that if the rotation of the board through a turn places the fin at a correspondingly high angle of attack, an area of very low pressure will develop around the leading edge of the fin and accelerate the board forward; the aforementioned effect provides an explanation for the greater speed of multi-finned type boards.
In terms of board design, however, it is equally important to note that the pressure differential between the leading and trailing sections of the airfoil in FIG. 1B is very large; hence, an airfoil at a high angle of attack tends to have a very large pitching moment (in the case of a wing) or yawing moment (in the case of a sail), the effects of which must be countered with considerable deflection of the elevator or rudder to maintain directional control. It can be assumed that the cambered side-fin foil at a similarly high angle of attack will also have a very large yawing moment, and that the yawing moment will be opposite the rotation of the turn. The reverse yawing moment of the side-fin in a turn provides an effective explanation for the poorly understood control problems exhibited by the original wide-tailed twin-fins and the very early double-finned fish style boards of the prior art.
As previously discussed, the “tracking” problems of the original double-finned boards were eliminated through trial and error, without benefit of the information provided in the discussion above. As a consequence, current multi-fin configurations retain a number of features that actually contribute to a marked increase in drag. The source of the drag is illustrated in more detail in FIG. 2, which depicts the bottom of a conventional tri-fin surfboard according to the prior art. As shown, the two side-fins are located on opposite sides of the board near the perimeter edge or “rail,” and well forward the center stabilizing fin at the tail. When the board is at speed on the wave and the rider's weight is neutrally centered on the board, the heading H of the board will cause a water-flow F that is substantially opposite the heading; when the water-flow F parallels the longitudinal centerline or stringer as shown, the negatively angled side-fin setting, which has a standard toe-in angle of approximately four degrees, causes the water-flow F to strike the outside, cambered surface of the side-fins (the side facing the perimeter edge or rail), and creates high drag due to the low-pressure area (depicted here as turbulence) that develops on the lee or inside surface of the side-fins (the side facing the longitudinal centerline or stringer).
FIG. 2A and FIG. 2B are closer, cross-section views depicting the cambered foil of prior art side-fins. The conventional flat-sided cambered foil of the prior art is shown in FIG. 2A; for a given thickness, the prior art foil shown in FIG. 2B has slightly increased camber due to the shallow concave of the inside surface. The views depict how the negative toe-in of the side-fin causes the water-flow F to strike the side-fins at an angle, which causes the water-flow on the lee or inside surface of the side-fins to tend to separate or become turbulent, and increases drag.
Note that the actual angle of the side-fin foil in FIG. 2A and FIG. 2B is equivalent to an aircraft flying upside down; since this is known to be an inefficient way to generate lift, it follows that the negatively angled side-fin setting will compromise the basic functions of the side-fin(s), which, as will be appreciated by persons skilled in the art after reading the disclosure which follows below, are as follows: the negative toe-in angle of the side-fins improves directional stability when the rider's weight is evenly balanced on the board; when the rider leans to turn the side-fin functions as a deflected rudder and aids the board's initial rotation and, as the prior art tri-fin (shown in FIG. 2) rotates further in the turn, the angle of the water flow changes so that it is striking the “underside” of the fin(s), which places the fins of the board at a high, “flying” angle of attack and, much like a sail, accelerates the board forward.
FIG. 3A shows the rotation of the board in more detail: in the diagram depicted, the rider's weight shift when leaning in a turn creates a yawing moment YM that, in relation to the board's original heading H, changes the angle of the “apparent” water-flow F striking the fins, and places the fins at a higher angle of attack. (Note: the term “apparent” water-flow is used in the same manner as the term “apparent wind” is used in sailing-from the board's perspective, the water is “apparently” moving, although the actual angle of the water-flow striking the fins is caused almost entirely by the motion of the board itself.) In the turn shown, an arrow H represents the board's original heading (shown in FIG. 2), while the three arrows running parallel to and in an opposite direction to the first arrow are used to represent the apparent water-flow F resulting from that heading. The board's rotation in the turn is referenced by an imaginary axis of rotation AR, and the arrows at either end of the board depict the direction and rotation R of the nose and tail of the board as the rider, leaning in the turn, shoves the tail in one direction, and causes the nose to move in the opposite direction. The view shows that the movement of the tail as the board rotates causes the fins at the rear of the board to be placed at a higher angle of attack relative to the water-flow F, and increases their potential “lift.” (The “lift” is depicted here as the pressure field described above. In addition, the rotation of the board and angle of attack of the fins may be better visualized if the view is assumed to be from the rider's perspective with the deck or top surface of the board transparent.)
FIG. 3B depicts a very early, and largely unsuccessful, split-tailed fish style board of the prior art, and shows that the same rotation on a board with a wide tail and correspondingly wide fin-spacing will place the side-fins at a higher angle of attack. The added problem is that on a wide-tailed board the side-fins are further away from the rider's feet—because the rider controls the board through weight shifts that are transmitted through the feet, it follows that a wide side-fin spacing will increase the moment arm of the side-fin, and that the added leverage will lead to control problems since the rider will be less able to counter the reverse yaw of the side-fins and maintain control of the board through a turn.
From the preceding discussion, it will also be apparent that increasing the length of the board or the speed at which it is ridden will exacerbate the problems outlined above. Persons knowledgeable in board design will note that the early double-finned fish style boards, which originally used the parallel side-fin setting shown in FIG. 3B and had large, low aspect ratio keel type fins, were limited to roughly five and a half feet in length. Although these boards at times exhibited exceptional speed in smaller surf, they became difficult or impossible to control at higher speeds in larger, faster waves, where the size of the board was typically increased. As a result, the parallel side-fin setting shown in FIG. 3B was quickly abandoned in favor of the negatively angled side-fin setting of the prior art. The early twin-fin style boards of the same era (not depicted) were also notoriously prone to tracking problems, particularly in larger surf. As will be appreciated by those of skill in the art after reading the disclosure below, this was due to the wide spacing of the side-fins, which were placed near the extreme edge of the very wide square tail and far from the rider's feet.
Therefore, when comparing the modern prior art tri-fin depicted in FIG. 2 and FIG. 3A to the early, wide-tailed fish of FIG. 3B, it can be seen that the design modifications have comprised a considerable narrowing of the tail; the side-fin placement has moved further forward on the board; and the side-fins are now universally set at a negative angle of attack. These design changes have had the effect of eliminating prior art control problems, but without first identifying their cause—the prior art tri-fin, which is considered to be a fast, exceptionally maneuverable board, retains the inherent drawbacks of the negatively angled side-fin setting, and suffers from seriously compromised performance and considerable unnecessary drag as a result.
Accordingly, much room remains for improvement in the structure and placement of fins and foils on surfboards.